The moves have come during a relatively robust period for going public, capped by Twitter's Sept. 12 announcement that it had filed for an initial public offering.

Brian Wieser, a senior analyst with Pivotal Research Group, said that market conditions generally make it an appropriate time for companies to consider an IPO.

"The markets are pretty robust right now, and the equity markets have held up through most of this year," said Wieser, who covers companies in the entertainment space. "The appetite is certainly generally positive for new issuances of all types."

But the Tokyo electronics and media giant said in an Aug. 6 letter addressed to Loeb that it "unanimously concluded that continuing to own 100% of our entertainment business is the best path forward."

With that matter settled -- at least for now -- here's a look at three private companies and their IPO plans (or lack thereof).

-- MGM Holdings Inc., the parent of Metro-Goldwyn-Mayer Inc., filed a draft registration statement for an initial public offering with the Securities and Exchange Commission in July 2012. But the film and television studio behind last year's "Skyfall" and "The Hobbit: An Unexpected Journey," did not move forward with an IPO. The company had filed as a so-called "emerging-growth company” -- an SEC classification that offers businesses with less than $1 billion in annual revenue to sidestep certain regulatory and filing requirements. In March, MGM reported 2012 revenue of $1.38 billion, invalidating the company's status as an "emerging-growth company." As a result, MGM would need to file a new draft registration statement before it could go public. Last week, MGM, whose stock is traded over the counter, announced a dividend designed to protect the company from a hostile takeover. The company declined to comment.

-- In June, electronic dance music promoter SFX Entertainment filed for an initial public offering to raise up to $175 million. New York-based SFX, which represents several festivals and music events, said in a regulatory filing that it planned to use proceeds generated by the offering to acquire other companies and expand its festival slate. Last year, SFX, founded by Robert F.X. Sillerman, generated revenue of $24.8 million but had a net loss of $16 million. The company's IPO is being underwritten by UBS Investment Bank, Barclays and Jefferies; SFX has said it would trade on the Nasdaq under the "SFXE" symbol.

-- AMC Entertainment, the second-largest movie theater company in the U.S., said in an August regulatory filing that it would seek to raise $400 million from an initial public offering. The company, owned by Dalian Wanda Group of China and based in Leawood, Kan., said it could use proceeds from the IPO to pay down debt and fund acquisitions. The company has made a handful of other attempts in the last five years or so to go public. AMC aborted prospective public offerings in 2007, 2008 and last year. For the six-month period ending June 30, the company's net income was $41.1 million -- double what it made during the same period a year earlier. Adriana S. de Lozada, an analyst with private company research firm PrivCo, said AMC is "ripe for an IPO.... You have a growth story that is not just about numbers. AMC has shown the public that it is the type of company that can adjust to market trends. People want a better theater experience and they have been adjusting to that."